Finite Group Databasebeta

← Group #72343269

Character table — Group #72343269

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100
size111111112222666666661212121212121212121212121212121216161616242424242424242432323232323232324848484848484848484848484848484848484848484848484848484848484848646464646464646464646464
order122244442244222244442222222244444444888822224444366612121212444444444444444444448888888888886612122424242424242424
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111
χ3111111111111111111111111111111111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ511111111-1-1-1-11-1-11-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-11111111111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1
χ611111111-1-1-1-11-1-11-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111-1-11111111111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1
χ711111111-1-1-1-11-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-11111111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1-1-1-1-1-1-11111
χ811111111-1-1-1-11-1-11-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-11111111111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ91111-1-1-1-111-1-11111-1-1-1-11-111-1-11-111-1-111-1-1i−ii−i1111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1ii−i−iii−i−ii−ii−ii−ii−ii−ii−i11-1-1ii−i−iii−i−i
χ101111-1-1-1-111-1-11111-1-1-1-11-111-1-11-111-1-111-1-1i−ii−i-1-1-1-111111111-1-1-1-1-11-11-1-111-1-111−i−iii−i−iii−ii−iii−ii−i−ii−ii11-1-1ii−i−iii−i−i
χ111111-1-1-1-111-1-11111-1-1-1-11-111-1-11-111-1-111-1-1−ii−ii1111-1-1-1-11111-1-1-1-11-11-111-1-111-1-1−i−iii−i−iii−ii−ii−ii−ii−ii−ii11-1-1−i−iii−i−iii
χ121111-1-1-1-111-1-11111-1-1-1-11-111-1-11-111-1-111-1-1−ii−ii-1-1-1-111111111-1-1-1-1-11-11-1-111-1-111ii−i−iii−i−ii−ii−i−ii−iii−ii−i11-1-1−i−iii−i−iii
χ131111-1-1-1-1-1-1111-1-1111-1-11-1-1-1111-111-1-1-1-111i−i−ii11-1-1-1-1111111-1-1-1-11-1-1111-1-1-1-111ii−i−i−i−iiii−i−iii−i−iii−i−ii-1-111ii−i−i−i−iii
χ141111-1-1-1-1-1-1111-1-1111-1-11-1-1-1111-111-1-1-1-111i−i−ii-1-11111-1-11111-1-1-1-1-111-1-1-11111-1-1−i−iiiii−i−i−iii−ii−i−ii−iii−i-1-111ii−i−i−i−iii
χ151111-1-1-1-1-1-1111-1-1111-1-11-1-1-1111-111-1-1-1-111−iii−i11-1-1-1-1111111-1-1-1-11-1-1111-1-1-1-111−i−iiiii−i−i−iii−i−iii−i−iii−i-1-111−i−iiiii−i−i
χ161111-1-1-1-1-1-1111-1-1111-1-11-1-1-1111-111-1-1-1-111−iii−i-1-11111-1-11111-1-1-1-1-111-1-1-11111-1-1ii−i−i−i−iiii−i−ii−iii−ii−i−ii-1-111−i−iiiii−i−i
χ17222222222222222222222222222222222222222200000000-1-1-1-1-1-1-1-100000000000000000000000022220000-1-1-1-1-1-1-1-1-1-1-1-1
χ18222222222222222222222222222222222222-2-2-2-200000000-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2-20000-1-1-1-111111111
χ1922222222-2-2-2-22-2-22-2-22222-2-2-2-2222222-2-2-2-222-2-200000000-1-1-1-1-1-1-1-100000000000000000000000022-2-200001111-1-1-1-11111
χ2022222222-2-2-2-22-2-22-2-22222-2-2-2-2222222-2-2-2-2-2-22200000000-1-1-1-1-1-1-1-1000000000000000000000000-2-222000011111111-1-1-1-1
χ212222-2-2-2-222-2-22222-2-2-2-22-222-2-22-222-2-222-2-22i−2i2i−2i00000000-1-1-1-111110000000000000000000000002i−2i2i−2i0000-1-111−i−iii−i−iii
χ222222-2-2-2-222-2-22222-2-2-2-22-222-2-22-222-2-222-2-2−2i2i−2i2i00000000-1-1-1-11111000000000000000000000000−2i2i−2i2i0000-1-111ii−i−iii−i−i
χ232222-2-2-2-2-2-2222-2-2222-2-22-2-2-2222-222-2-2-2-2222i−2i−2i2i00000000-1-1-1-111110000000000000000000000002i−2i−2i2i000011-1-1−i−iiiii−i−i
χ242222-2-2-2-2-2-2222-2-2222-2-22-2-2-2222-222-2-2-2-222−2i2i2i−2i00000000-1-1-1-11111000000000000000000000000−2i2i2i−2i000011-1-1ii−i−i−i−iii
χ252-2-2222-2-22-22-2-22-222-22-2-222-22-22-22-22-22-22-20000000000002-2-22-2-222000000000000000000000000000000002-22-200000000
χ262-2-2222-2-22-22-2-22-222-22-2-222-22-22-22-22-22-22-2000000000000-111-111-1-100000000000000000000000000000000-11-11−i3i3−i3i3−i3i3−i3i3
χ272-2-2222-2-22-22-2-22-222-22-2-222-22-22-22-22-22-22-2000000000000-111-111-1-100000000000000000000000000000000-11-11i3−i3i3−i3i3−i3i3−i3
χ282-2-2222-2-2-22-22-2-222-222-2-22-22-222-22-22-2-22-220000000000002-2-22-2-22200000000000000000000000000000000-22-2200000000
χ292-2-2222-2-2-22-22-2-222-222-2-22-22-222-22-22-2-22-22000000000000-111-111-1-1000000000000000000000000000000001-11-1−i3i3−i3i3i3−i3i3−i3
χ302-2-2222-2-2-22-22-2-222-222-2-22-22-222-22-22-2-22-22000000000000-111-111-1-1000000000000000000000000000000001-11-1i3−i3i3−i3−i3i3−i3i3
χ312-2-22-2-2222-2-22-22-22-22-22-2-22-2-22222-2-222-2-220000000000002-2-2222-2-2000000000000000000000000000000002-2-2200000000
χ322-2-22-2-2222-2-22-22-22-22-22-2-22-2-22222-2-222-2-22000000000000-111-1-1-11100000000000000000000000000000000-111-13−3−333−3−33
χ332-2-22-2-2222-2-22-22-22-22-22-2-22-2-22222-2-222-2-22000000000000-111-1-1-11100000000000000000000000000000000-111-1−333−3−333−3
χ342-2-22-2-222-222-2-2-2222-2-22-2-2-222-2222-2-22-222-20000000000002-2-2222-2-200000000000000000000000000000000-222-200000000
χ352-2-22-2-222-222-2-2-2222-2-22-2-2-222-2222-2-22-222-2000000000000-111-1-1-111000000000000000000000000000000001-1-113−3−33−333−3
χ362-2-22-2-222-222-2-2-2222-2-22-2-2-222-2222-2-22-222-2000000000000-111-1-1-111000000000000000000000000000000001-1-11−333−33−3−33
χ3733333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1333311111111000000001111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111000000000000
χ3833333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-100000000-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ3933333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-311111111000000001111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1000000000000
χ4033333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-3-3-3-3-1-1-1-1-1-1-1-100000000-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111000000000000
χ4133333333-3-3-3-33-3-33-3-333-1-11111-1-1-1-1-1-1111133-3-311-1-111-1-10000000011-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1000000000000
χ4233333333-3-3-3-33-3-33-3-333-1-11111-1-1-1-1-1-1111133-3-3-1-111-1-11100000000-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111000000000000
χ4333333333-3-3-3-33-3-33-3-333-1-11111-1-1-1-1-1-11111-3-33311-1-111-1-10000000011-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111000000000000
χ4433333333-3-3-3-33-3-33-3-333-1-11111-1-1-1-1-1-11111-3-333-1-111-1-11100000000-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1000000000000
χ453333-3-3-3-333-3-33333-3-3-3-3-11-1-111-11-1-111-1-1113i−3i3i−3i1111-1-1-1-1000000001-11-1-1-111-1-111−i−iii−i−iiii−ii−i−ii−iii−ii−i000000000000
χ463333-3-3-3-333-3-33333-3-3-3-3-11-1-111-11-1-111-1-1113i−3i3i−3i-1-1-1-1111100000000-11-1111-1-111-1-1ii−i−iii−i−i−ii−ii−ii−ii−ii−ii000000000000
χ473333-3-3-3-333-3-33333-3-3-3-3-11-1-111-11-1-111-1-111−3i3i−3i3i1111-1-1-1-1000000001-11-1-1-111-1-111ii−i−iii−i−i−ii−iii−ii−i−ii−ii000000000000
χ483333-3-3-3-333-3-33333-3-3-3-3-11-1-111-11-1-111-1-111−3i3i−3i3i-1-1-1-1111100000000-11-1111-1-111-1-1−i−iii−i−iiii−ii−ii−ii−ii−ii−i000000000000
χ493333-3-3-3-3-3-3333-3-3333-3-3-1111-1-1-11-1-11111-1-13i−3i−3i3i11-1-1-1-111000000001-1-11-1-11111-1-1−i−iiiii−i−ii−i−ii−iii−ii−i−ii000000000000
χ503333-3-3-3-3-3-3333-3-3333-3-3-1111-1-1-11-1-11111-1-13i−3i−3i3i-1-11111-1-100000000-111-111-1-1-1-111ii−i−i−i−iii−iii−i−iii−i−iii−i000000000000
χ513333-3-3-3-3-3-3333-3-3333-3-3-1111-1-1-11-1-11111-1-1−3i3i3i−3i11-1-1-1-111000000001-1-11-1-11111-1-1ii−i−i−i−iii−iii−ii−i−ii−iii−i000000000000
χ523333-3-3-3-3-3-3333-3-3333-3-3-1111-1-1-11-1-11111-1-1−3i3i3i−3i-1-11111-1-100000000-111-111-1-1-1-111−i−iiiii−i−ii−i−iii−i−iii−i−ii000000000000
χ53666666666666-2-2-2-2-2-2-2-22-222-2-22-2-2-222-2-22200002222222200000000-2-2-2-20000000000000000000000000000000000000000
χ54666666666666-2-2-2-2-2-2-2-22-222-2-22-2-2-222-2-2220000-2-2-2-2-2-2-2-20000000022220000000000000000000000000000000000000000
χ55666666666666-2-2-2-2-2-2-2-2-22-2-222-2222-2-222-2-2000000000000000000000000000000000000000022220000-2-2-2-2000000000000
χ56666666666666-2-2-2-2-2-2-2-2-22-2-222-2222-2-222-2-20000000000000000000000000000000000000000-2-2-2-200002222000000000000
χ5766666666-6-6-6-6-222-222-2-22-2-2-2222-2-2-22222-2-2000022-2-222-2-200000000-2-2220000000000000000000000000000000000000000
χ5866666666-6-6-6-6-222-222-2-22-2-2-2222-2-2-22222-2-20000-2-222-2-2220000000022-2-20000000000000000000000000000000000000000
χ5966666666-6-6-6-6-222-222-2-2-2222-2-2-2222-2-2-2-222000000000000000000000000000000000000000022-2-20000-2-222000000000000
χ6066666666-6-6-6-6-222-222-2-2-2222-2-2-2222-2-2-2-2220000000000000000000000000000000000000000-2-222000022-2-2000000000000
χ616666-6-6-6-666-6-6-2-2-2-2222222222222-2-2-2-2-2-2-2-200002222-2-2-2-200000000-22-220000000000000000000000000000000000000000
χ626666-6-6-6-666-6-6-2-2-2-2222222222222-2-2-2-2-2-2-2-20000-2-2-2-22222000000002-22-20000000000000000000000000000000000000000
χ636666-6-6-6-666-6-6-2-2-2-22222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000002i−2i2i−2i0000−2i2i−2i2i000000000000
χ646666-6-6-6-666-6-6-2-2-2-22222-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000−2i2i−2i2i00002i−2i2i−2i000000000000
χ656666-6-6-6-6-6-666-222-2-2-22222-2-2-2-222-2-2-2-22222000022-2-2-2-22200000000-222-20000000000000000000000000000000000000000
χ666666-6-6-6-6-6-666-222-2-2-22222-2-2-2-222-2-2-2-222220000-2-22222-2-2000000002-2-220000000000000000000000000000000000000000
χ676666-6-6-6-6-6-666-222-2-2-222-2-22222-2-22222-2-2-2-200000000000000000000000000000000000000002i−2i−2i2i0000−2i2i2i−2i000000000000
χ686666-6-6-6-6-6-666-222-2-2-222-2-22222-2-22222-2-2-2-20000000000000000000000000000000000000000−2i2i2i−2i00002i−2i−2i2i000000000000
χ696-6-6666-6-66-66-62-22-2-22-2222-222-2-2-22-2-222-2-22000000000000000000000000000000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ706-6-6666-6-66-66-62-22-2-22-2222-222-2-2-22-2-222-2-2200000000000000000000000000000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ716-6-6666-6-66-66-62-22-2-22-22-2-22-2-2222-222-2-222-20000000000000000000000002-22-22-22-200000000000000000000000000000000
χ726-6-6666-6-66-66-62-22-2-22-22-2-22-2-2222-222-2-222-2000000000000000000000000-22-22-22-2200000000000000000000000000000000
χ736-6-6666-6-66-66-6-66-666-66-62-2-22-22-22-22-22-22-220000000000000000000000000000000000000000000000000000000000000000
χ746-6-6666-6-6-66-6622-2-22-2-22222-2-22-2-22-2-22-222-2000000000000000000000000000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ756-6-6666-6-6-66-6622-2-22-2-22222-2-22-2-22-2-22-222-200000000000000000000000000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ766-6-6666-6-6-66-6622-2-22-2-22-2-2-222-222-222-22-2-220000000000000000000000002-22-2-22-2200000000000000000000000000000000
χ776-6-6666-6-6-66-6622-2-22-2-22-2-2-222-222-222-22-2-22000000000000000000000000-22-222-22-200000000000000000000000000000000
χ786-6-6666-6-6-66-66-6-666-666-62-22-22-2-22-22-222-22-20000000000000000000000000000000000000000000000000000000000000000
χ796-6-66-6-6666-6-662-22-22-22-22-2-22-22-222-22-22-22-2000000000000000000000000000000002-2-222-2-22000000000000000000000000
χ806-6-66-6-6666-6-662-22-22-22-22-2-22-22-222-22-22-22-200000000000000000000000000000000-222-2-222-2000000000000000000000000
χ816-6-66-6-6666-6-662-22-22-22-2-222-22-22-2-22-22-22-220000000000000000000000002-2-222-2-2200000000000000000000000000000000
χ826-6-66-6-6666-6-662-22-22-22-2-222-22-22-2-22-22-22-22000000000000000000000000-222-2-222-200000000000000000000000000000000
χ836-6-66-6-6666-6-66-66-66-66-6622-222-2-2-2-222-2-222-20000000000000000000000000000000000000000000000000000000000000000
χ846-6-66-6-666-666-622-2-2-222-22-22-22-2-222-22-2-22-22000000000000000000000000000000002-2-22-222-2000000000000000000000000
χ856-6-66-6-666-666-622-2-2-222-22-22-22-2-222-22-2-22-2200000000000000000000000000000000-222-22-2-22000000000000000000000000
χ866-6-66-6-666-666-622-2-2-222-2-22-22-222-2-22-222-22-20000000000000000000000002-2-22-222-200000000000000000000000000000000
χ876-6-66-6-666-666-622-2-2-222-2-22-22-222-2-22-222-22-2000000000000000000000000-222-22-2-2200000000000000000000000000000000
χ886-6-66-6-666-666-6-6-6666-6-66222-2-22-2-2-222-22-2-220000000000000000000000000000000000000000000000000000000000000000
χ8988-8-88i−8i8i−8i00000000000000000000000000000000004-4004i−4i22-2-22i−2i2i−2i00000000000000000000000000000000000000000000
χ9088-8-88i−8i8i−8i0000000000000000000000000000000000-4400−4i4i22-2-22i−2i2i−2i00000000000000000000000000000000000000000000
χ9188-8-8−8i8i−8i8i00000000000000000000000000000000004-400−4i4i22-2-2−2i2i−2i2i00000000000000000000000000000000000000000000
χ9288-8-8−8i8i−8i8i0000000000000000000000000000000000-44004i−4i22-2-2−2i2i−2i2i00000000000000000000000000000000000000000000
χ938-88-88i−8i−8i8i000000000000000000000000000000004-4004i−4i002-22-2−2i2i2i−2i00000000000000000000000000000000000000000000
χ948-88-88i−8i−8i8i00000000000000000000000000000000-4400−4i4i002-22-2−2i2i2i−2i00000000000000000000000000000000000000000000
χ958-88-8−8i8i8i−8i000000000000000000000000000000004-400−4i4i002-22-22i−2i−2i2i00000000000000000000000000000000000000000000
χ968-88-8−8i8i8i−8i00000000000000000000000000000000-44004i−4i002-22-22i−2i−2i2i00000000000000000000000000000000000000000000
χ971616-16-1616i−16i16i−16i0000000000000000000000000000000000000000-2-222−2i2i−2i2i00000000000000000000000000000000000000000000
χ981616-16-16−16i16i−16i16i0000000000000000000000000000000000000000-2-2222i−2i2i−2i00000000000000000000000000000000000000000000
χ9916-1616-1616i−16i−16i16i0000000000000000000000000000000000000000-22-222i−2i−2i2i00000000000000000000000000000000000000000000
χ10016-1616-16−16i16i16i−16i0000000000000000000000000000000000000000-22-22−2i2i2i−2i00000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).